# Regular Languages Livestream.pdf -

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Theory of Computation 1 4 Regular Languages II Nov Free Languages 15 Nov Context Decidability 22 Nov 1 MY Nov Undecidability 29 unsolvable problems There are uncountable may countably many possible problems possible algos what is a computer T'tp tcompu L O outputs inputs I Restrict input I 0110100 multiplexing IO 0 II input 2 Io input Jt 44 Can assume I single input one bit of output 2 of state charges instruction Cpu system possibly Assumptions a fixed internal memory machine stops done reading input bi once in some state C Machine starts State names Example fy wide circle I 1 is a t state start stoles stole a Example transitions O only input 00 tension Example o Every state E na est Iff't fo accept ufI www.oiIS has I accept lion empty string possible tryinputs C A Deterministic Finite Automaton DFA following attributes has the I Q finite set of States input alphabet 2 Ei finite the stat state 3 Co E Q states set of final 4 F E Q transition function 5 S is a total 8 Q X E Q function f every possible to statelinput pair state we what are in read is defined Define formally co_ Q 90,91 92,933 8 20,13 Iff't Iff't go F Eo 9 92 0 Transition Table 91 90 gIĀµ 97 90 92 93 93 I 92 I 91 Defs DFA M on input w computation of of slates visited sequence repeat states can if a computation is accepting is in F last state a language is a set of strings can be infinite finite or language if it is the a language is regular of Sony DFA I that computation set of strings have on accepting over I all strings L E soit's length I havingodd Lis regular Ex over 83 E all strings regular 29197 hors empty set rain g chars Ei't Ee in a nonempty all strings Set Operations languages reg on of languages be a set Let under operation C is closed in C Say to languages is in C that if applying in a language resu